Team, Visitors, External Collaborators
Overall Objectives
Research Program
Highlights of the Year
New Software and Platforms
New Results
Partnerships and Cooperations
Dissemination
Bibliography
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Bibliography

Major publications by the team in recent years
[1]
E. Bayer-Fluckiger, J.-P. Cerri, J. Chaubert.
Euclidean minima and central division algebras, in: International Journal of Number Theory, 2009, vol. 5, no 7, pp. 1155–1168.
http://www.worldscinet.com/ijnt/05/0507/S1793042109002614.html
[2]
K. Belabas, M. Bhargava, C. Pomerance.
Error estimates for the Davenport-Heilbronn theorems, in: Duke Mathematical Journal, 2010, vol. 153, no 1, pp. 173–210.
http://projecteuclid.org/euclid.dmj/1272480934
[3]
X. Caruso, J. L. Borgne.
A new faster algorithm for factoring skew polynomials over finite fields, in: J. Symbolic Comput., 2018, vol. 79, pp. 411–443.
[4]
X. Caruso, D. Roe, T. Vaccon.
Tracking p-adic precision, in: LMS J. Comput. Math., 2014, vol. 17, pp. 274–294.
[5]
G. Castagnos, F. Laguillaumie, I. Tucker.
Practical Fully Secure Unrestricted Inner Product Functional Encryption modulo p, in: Advances in Cryptology – ASIACRYPT 2018, Part II, T. Peyrin, S. Galbraith (editors), Lecture Notes in Computer Science, International Association for Cryptologic Research, 2018, vol. 11273, pp. 733–764.
[6]
H. Cohen, F. Strömberg.
Modular Forms: A Classical Approach, Graduate Studies in Mathematics, American Mathematical Society, 2017, vol. 179.
http://bookstore.ams.org/gsm-179/
[7]
J.-M. Couveignes, B. Edixhoven.
Computational aspects of modular forms and Galois representations, Princeton University Press, 2011.
[8]
A. Enge, P. Gaudry, E. Thomé.
An L(1/3) Discrete Logarithm Algorithm for Low Degree Curves, in: Journal of Cryptology, 2011, vol. 24, no 1, pp. 24–41.
[9]
A. Enge, W. Hart, F. Johansson.
Short addition sequences for theta functions, in: Journal of Integer Sequences, 2018, vol. 18, no 2, pp. 1–34.
[10]
D. Lubicz, D. Robert.
Computing isogenies between abelian varieties, in: Compositio Mathematica, 09 2012, vol. 148, no 05, pp. 1483–1515.
http://dx.doi.org/10.1112/S0010437X12000243
Publications of the year

Doctoral Dissertations and Habilitation Theses

[11]
G. Castagnos.
Cryptography based on quadratic fields: cryptanalyses, primitives and protocols, Université de Bordeaux, November 2019, Habilitation à diriger des recherches.
https://tel.archives-ouvertes.fr/tel-02403707

Articles in International Peer-Reviewed Journals

[12]
R. Barbulescu, J. Ray.
Numerical verification of the Cohen-Lenstra-Martinet heuristics and of Greenberg's p-rationality conjecture, in: Journal de Théorie des Nombres de Bordeaux, 2019, forthcoming.
https://hal.archives-ouvertes.fr/hal-01534050
[13]
A. Bartel, A. Page.
Group representations in the homology of 3-manifolds, in: Commentarii Mathematici Helvetici, March 2019, https://arxiv.org/abs/1605.04866. [ DOI : 10.4171/CMH/455 ]
https://hal.inria.fr/hal-01671748
[14]
K. Belabas, D. Bernardi, B. Perrin-Riou.
La constante de Manin et le degré modulaire d'une courbe elliptique, in: Publications Mathématiques de Besançon : Algèbre et Théorie des Nombres, 2019, no 2, pp. 81-103.
https://hal.archives-ouvertes.fr/hal-01766202
[15]
J.-P. Cerri, P. Lezowski.
Computation of Euclidean minima in totally definite quaternion fields, in: International Journal of Number Theory, 2019, vol. 15, no 1, pp. 43–66.
https://hal.archives-ouvertes.fr/hal-01447059
[16]
S. Ionica, E. Thomé.
Isogeny graphs with maximal real multiplication, in: Journal of Number Theory, February 2020, vol. 207, pp. 385-422, https://arxiv.org/abs/1407.6672. [ DOI : 10.1016/j.jnt.2019.06.019 ]
https://hal.archives-ouvertes.fr/hal-00967742
[17]
F. Johansson, I. V. Blagouchine.
Computing Stieltjes constants using complex integration, in: Mathematics of Computation, 2019, vol. 88, no 318, https://arxiv.org/abs/1804.01679.
https://hal.inria.fr/hal-01758620
[18]
A. Riffaut.
Equations with powers of singular moduli, in: International Journal of Number Theory, 2019, vol. 15, no 3, pp. 445-468. [ DOI : 10.1142/S1793042119500234 ]
https://hal.archives-ouvertes.fr/hal-01630363

International Conferences with Proceedings

[19]
X. Caruso, T. Vaccon, T. Verron.
Gröbner bases over Tate algebras, in: ISSAC, Beijing, China, July 2019, https://arxiv.org/abs/1901.09574. [ DOI : 10.1145/3326229.3326257 ]
https://hal.archives-ouvertes.fr/hal-01995881
[20]
G. Castagnos, D. Catalano, F. Laguillaumie, F. Savasta, I. Tucker.
Two-Party ECDSA from Hash Proof Systems and Efficient Instantiations, in: CRYPTO 2019 - 39th Annual International Cryptology Conference, Santa Barbara, United States, Advances in Cryptology – CRYPTO 2019, August 2019, vol. LNCS, no 11694, pp. 191-221. [ DOI : 10.1007/978-3-030-26954-8_7 ]
https://hal.archives-ouvertes.fr/hal-02281931
[21]
Best Paper
F. Johansson.
Faster arbitrary-precision dot product and matrix multiplication, in: 26th IEEE Symposium on Computer Arithmetic (ARITH26), Kyoto, Japan, June 2019, https://arxiv.org/abs/1901.04289.
https://hal.inria.fr/hal-01980399

Scientific Books (or Scientific Book chapters)

[22]
X. Caruso.
An introduction to p-adic period rings, in: An introduction to p-adic Hodge theory, 2019, https://arxiv.org/abs/1908.08424, forthcoming.
https://hal.archives-ouvertes.fr/hal-02268787
[23]
H. Cohen.
An Introduction to Modular Forms, in: Notes from the International School on Computational Number Theory, I. Inam, E. Büyükaşık (editors), Tutorials, Schools, and Workshops in the Mathematical Sciences, Birkhäuser, 2019, pp. 3-62, https://arxiv.org/abs/1809.10907.
https://hal.inria.fr/hal-01883058
[24]
H. Cohen.
Computational Number Theory in Relation with L-Functions, in: Notes from the International School on Computational Number Theory, I. Inam, E. Büyükaşık (editors), Tutorials, Schools, and Workshops in the Mathematical Sciences, Birkhäuser, 2019, pp. 171-266, https://arxiv.org/abs/1809.10904. [ DOI : 10.1007/978-3-030-12558-5_3 ]
https://hal.inria.fr/hal-01883052
[25]
H. Cohen.
Expansions at Cusps and Petersson Products in Pari/GP, in: Elliptic Integrals, Elliptic Functions and Modular Forms in Quantum Field Theory, J. Blümlein, C. Schneider, P. Paule (editors), Texts & Monographs in Symbolic Computation, Springer, 2019, https://arxiv.org/abs/1809.10908.
https://hal.inria.fr/hal-01883070
[26]
F. Johansson.
Numerical Evaluation of Elliptic Functions, Elliptic Integrals and Modular Forms, in: Elliptic Integrals, Elliptic Functions and Modular Forms in Quantum Field Theory, J. Blümlein, C. Schneider, P. Paule (editors), Texts & Monographs in Symbolic Computation, Springer, 2019, pp. 269-293, https://arxiv.org/abs/1806.06725.
https://hal.inria.fr/hal-01817952

Other Publications

[27]
R. Barbulescu, N. El Mrabet, L. Ghammam.
A taxonomy of pairings, their security, their complexity, May 2019, working paper or preprint.
https://hal.archives-ouvertes.fr/hal-02129868
[28]
R. Barbulescu, S. Shinde.
A classification of ECM-friendly families using modular curves, February 2019, working paper or preprint.
https://hal.archives-ouvertes.fr/hal-01822144
[29]
X. Caruso.
Residues of skew rational functions and linearized Goppa codes, August 2019, https://arxiv.org/abs/1908.08430 - working paper or preprint.
https://hal.archives-ouvertes.fr/hal-02268790
[30]
J.-M. Couveignes.
Enumerating number fields, November 2019, https://arxiv.org/abs/1907.13617 - working paper or preprint.
https://hal.archives-ouvertes.fr/hal-02375397
[31]
J. Kieffer.
Degree and height estimates for modular equations on PEL Shimura varieties, January 2020, https://arxiv.org/abs/2001.04138 - working paper or preprint.
https://hal.archives-ouvertes.fr/hal-02436057
[32]
J. Kieffer, A. Page, D. Robert.
Computing isogenies from modular equations between Jacobians of genus 2 curves, January 2020, https://arxiv.org/abs/2001.04137 - working paper or preprint.
https://hal.archives-ouvertes.fr/hal-02436133
[33]
C. Maire, A. Page.
Codes from unit groups of division algebras over number fields, 2019, https://arxiv.org/abs/1804.07108 - working paper or preprint.
https://hal.inria.fr/hal-01770396
[34]
C. Martindale.
Hilbert Modular Polynomials, January 2019, working paper or preprint.
https://hal.inria.fr/hal-01990298
[35]
E. Milio, D. Robert.
Modular polynomials on Hilbert surfaces, June 2019, working paper or preprint.
https://hal.archives-ouvertes.fr/hal-01520262
References in notes
[36]
K. Belabas.
L'algorithmique de la théorie algébrique des nombres, in: Théorie algorithmique des nombres et équations diophantiennes, N. Berline, A. Plagne, C. Sabbah (editors), 2005, pp. 85–155.
[37]
H. Cohen, P. Stevenhagen.
Computational class field theory, in: Algorithmic Number Theory — Lattices, Number Fields, Curves and Cryptography, J. Buhler, P. Stevenhagen (editors), MSRI Publications, Cambridge University Press, 2008, vol. 44.
[38]
A. Enge.
Courbes algébriques et cryptologie, Université Denis Diderot, Paris 7, 2007, Habilitation à diriger des recherches.
http://tel.archives-ouvertes.fr/tel-00382535/en/